Orange High School. Year 8 Mathematics. Assignment 1
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1 Full name: Teacher: Due date: Orange High School Year 8 Mathematics Assignment
2 Syllabus Outcomes This assignment will address many outcomes from the Stage 4 syllabus, with particular focus on: Calculates the perimeters of plane shapes and the circumferences of circles MA4-12MG Uses formulas to calculate the areas of quadrilaterals and circles, and converts between units of area MA4-13MG Uses formulas to calculate the volumes of prisms and cylinders, and converts between units of volume MA4-14MG Communicates and connects mathematical ideas using appropriate terminology, diagrams and symbols MA4-1WM Applies appropriate mathematical techniques to solve problems MA4-2WM Gardner s Multiple Intelligences and Revised Blooms Taxonomy This assignment is designed to give all students an opportunity to demonstrate their best ability in Mathematics. Students can choose from tasks aligned to the different categories of Gardner s Multiple intelligences. The tasks are also aligned to the Revised Bloom's Taxonomy - a multi-tiered model of classifying thinking according to six cognitive levels of complexity. Thus, students can choose tasks according to their preferred modes of learning, or try different styles of learning. Students are able to revise and explore key concepts of this unit by completing lower-order tasks and then challenge themselves to develop their understanding and skills by completing higher-order tasks. Instructions You do not have to answer all the questions! Each box in the Task Grid (on the next page) is a task. 1. All students must complete tasks worth 25 marks. 2. 8MA1, 8MA2 and 8MA5 must include at least 2 tasks from the Creating and Evaluating columns as part of their 25 marks. 3. Most tasks will require you to write your answers on separate paper that you will then need to submit with your assignment. Please clearly write your full name and the task number on each piece of paper. Marks are awarded based on the difficulty and amount of work required to complete each task: Knowing and Understanding tasks (i.e. the first 2 columns) are worth 1 mark. Applying and Analysing tasks (i.e. the middle 2 columns) are work 2 marks. Creating and Evaluating tasks (i.e. the last 2 columns) are worth 3 marks. Page Assignment 1 Year 8 Mathematics
3 Task Grid Multiple Intelligences Verbal/Linguistic I enjoy reading, writing & speaking Logical/ Mathematical I enjoy working with numbers & science Visual/Spatial I enjoy painting, drawing & visualising Bodily/Kinesthetic I enjoy doing handson activities, sports & dance Musical/Rhythmic I enjoy making & listening to music Technology I enjoy using computers Bloom s Taxonomy: Six Thinking Levels Knowing Understanding Applying Analysing Creating Evaluating 1. Area of a Cross-Section 2. Converting Units of Area 3. Comparing Volumes 7. Area 8. Volume 9. Rates 13. Identify Shapes 14. Draw a Trapezium 19. Which Solid? 20. Similar Solids 25. Define Hypotenuse 31. List Special Quadrilaterals 26. Label Sides 32. Find Parallelograms 15. Calculate Area 21. Volume of a Solid 27. Calculate the Missing Side Length 33. Cargo Boxes 4. Fill Rates 5. Story of Units 10. Slowest and Fastest 16. Compare Rooms 11. Create a Jam Jar 17. Design a House 6. Height vs Volume 12. Who Am I? 18. Platinum Puzzle 22. Net of a Solid 23. Build a Solid 24. Compare Solids 28. Compare Methods 34. Good Bridge Design 29. Write a Song 35. Bad Bridge Design 30. Evaluate Videos 36. Cargo Boxes 1 mark 2 marks 3 marks Page Assignment 1 Year 8 Mathematics
4 Task Details Verbal/Linguistic A large trough is constructed from the diagram below. All dimensions are in metres. 1) Area of a Cross-Section Consider the shape of the cross section. Write the formula for the area of the cross section using only words. Formula correct and only in words 2) Converting Units of Area Explain the steps required to convert the area of the cross section from square metres into square centimetres. Steps correct and only in words 3) Comparing Volumes If the trough is filled until the water level is half way up the side (as shown in the diagram at the start of this section), what percentage of the trough will be filled with water? Show all your working. Hint: it is not 50%. Correct calculation of area or volume Correct calculation of percentage 4) Fill Rate The trough is filled with water at a rate of 250 Litres per minute. How long would it take to fill the trough to 80% of its capacity? Show all your working. Correct calculation of volume Correct calculation of time Page Assignment 1 Year 8 Mathematics
5 5) Story of Units Write a story about a farmer who used the incorrect units when calculating the volume of the trough and left the water on too long. The story must be approximately words and include mathematical calculations. Interesting story with beginning, climax and resolution. Correct length. Literacy including spelling and grammar Correct calculations 6) Height vs Volume Imagine you are watching the trough being filled with water at a constant rate. Describe how the height of the water would change over time. Use a graph to help illustrate your answer. Correct description of water height for trough Correct graph using height vs time Neat graph including all required labels Logical/Mathematical A series of jam jars look like letters when viewed face-on. They are 1cm thick, and the corners of the vessels have either whole or half centimetre values for their coordinates. 7) Area One of the jam jars is in the shape of the letter I. What is the area of the face which has been shaded? Correct area Page Assignment 1 Year 8 Mathematics
6 8) Volume One of the jam jars is in the shape of the letter L. What is the volume of this jam jar? Show your working. Correct volume 9) Rates Jam is poured into each vessel at a rate of 1 cm 3 per second. How long would it take to fill the jam jar in the shape of the letter O? Show your working. Correct volume Correct time 10) Slowest and Fastest Jam is poured into each vessel at a rate of 1 cm 3 per second. Which of the jam jars would be slowest to fill up? Which jam jar would fill up the fastest? Show all your working. Correct selection of slowest to fill jar Correct selection of fastest to fill jar 11) Create a Jam Jar Draw a 3D diagram of a Jam Jar on grid paper. The jar must be in the shape of a letter of the alphabet that has not already been used in the diagram above. Construct a graph of Height against Time showing how the height of jam would change as your Jar is filled (see below for an example). Accurate and neat drawing of unused letter Neat graph, labelled correctly Accurate graph Page Assignment 1 Year 8 Mathematics
7 12) Who Am I? The height of the jam in one of the jars above is measured and a graph of the height against time is plotted, as follows. Which jam jar does this chart represent? On the correct jam jar diagram, show which parts of the jar correspond to each straight line section of the graph (that is, what sections of the jar are being filled at what time). Hints: There are 4 straight line sections, starting at 0, 3, 7 and 11 seconds. You could use colour to code your answer. Note: The jar is filled through one hole only. Explain how the graph is useful in determining which jar is being filled. Correct Jam Jar selected Correct labelling of sections 1 & 2 Correct labelling of sections 3 & 4 Page Assignment 1 Year 8 Mathematics
8 Visual/Spatial These tasks are based on the following house design. 13) Identify Shapes On the house diagram, use a marker to outline and label at least three different types of shapes that can be seen. 3 different shapes outlined and labelled 14) Draw a Trapezium On the diagram of the house, use a marker to outline a trapezium at the end of the kitchen, adjacent to the lounge. Trapezium clearly identified Page Assignment 1 Year 8 Mathematics
9 15) Calculate Area Calculate the area of the Lounge. Show all your working. Clearly identifies how the lounge is composed of simpler shapes Correct calculation of the area 16) Compare Rooms Compare the size of the WIR to the Master Bedroom. What percentage of the size of the Master Bedroom is the WIR? Show all steps in your working. Correct area of each room Correct percentage 17) Design a House Design another simple three-bedroom house using a pencil and grid paper. Write the real life measurements. Include windows, doors, cupboards, bath, benches and other features to make it similar in detail to the diagram on page 8. You must make one room exactly double the size of another room. Indicate these rooms in your answer. Neat design using pencil and grid paper (not printed) Detailed design with three bedrooms One room double another and clearly labelled 18) Platinum Puzzle Platinum is a very rare metal, even rarer than gold. Its density is 21.5 g/cm 3. Assuming that the world production has been about 110 tonnes for each of the past 50 years, and negligible before that, which of the following has a comparable volume to that of the total amount of platinum ever produced? Include all steps of working out and thought processes in your answer. A) a shoe box, B) a cupboard C) a house D) Buckingham Palace E) the Grand Canyon Accurate calculation of Platinum quantity over 50 years Correct conversion between units Correct estimation of each objects volume Page Assignment 1 Year 8 Mathematics
10 Bodily/Kinesthetic Choose a box of food from your home pantry to help you answer these tasks. The tasks below will refer to this as the solid or your chosen box of food. 19) Which Solid? Look at your chosen box of food. Write down the mathematical name for this type of solid. List the number of faces, edges and vertices. Correct mathematical name and correct number of faces, edges and vertices 20) Similar Solids Look at your chosen box of food. Find four different examples of this type of solid that do not contain food. Look in your home, neighbourhood or school. Take a photo of each one and present these as a collage. Four different types supplied that do not contain food 21) Volume of a Solid Measure the dimensions of your chosen box of food. Make a 3-D sketch of your chosen box of food and label the dimension lengths. Calculate the volume of your chosen box of food. Show all working. Neat sketch showing all dimensions Correct volume 22) Net of a Solid Look at your chosen box of food. Draw a life size net of the solid. Use a ruler and the scale 1:1. Correct number and shape of faces Neat drawing showing all dimensions to scale 23) Build a Solid Build a triangular prism that has a similar volume to your chosen box of food. Mark the dimensions on your prism. The volume of your prism should be within 5 cubic centimetres of the capacity of your chosen box of food. A triangular prism Neat and accurately labelled with length of base and height of triangular cross-section and height/depth of prism The two volumes are equivalent Page Assignment 1 Year 8 Mathematics
11 24) Compare Solids If you created a triangular prism with the same volume and from the same material as your chosen box of food, which container would be more economical to produce? Explain your answer showing all working. Explain at least one other factor that companies need to consider when choosing the shape of their food container. Correct calculation of surface area Literacy including spelling and grammar Relevant alternative factor provided Musical/Rhythmic Listen to the, The Best Pythagorean Theorem Rap Ever ( on YouTube to complete these tasks. 25) Define Hypotenuse Write the definition of Hypotenuse used in the song. Write the exact words that they sing. Definition matches song s definition 26) Label Sides Label the sides of these right-angled triangles with the letters a, b, and c like they do in the song. Sides of each triangle accurately labelled including the side labelled with c 27) Calculate the Missing Side Length Calculate the length of the missing side in this triangle. Show your working out, like they do in the song. Correct side length Working matches the song s method of working Page Assignment 1 Year 8 Mathematics
12 28) Compare Methods Compare and contrast the methods for calculating the length of the Hypotenuse and finding the length one of a shorter side (or leg). Steps that are the same Steps that are different Accurate description of 2 or more similarities Accurate description of 2 or more differences 29) Write a Song Write a short song to teach Pythagoras Theorem to a Year 6 class. Record your song as an audio or video file and submit on a thumb drive. Keep your song to less than 2 minutes. Lyrics are clear and easy to follow/cohesive Lyrics are accurate and cover all processes of Pythagoras Theorem Music/lyrics are engaging 30) Evaluate Videos Find another video that teaches Pythagoras Theorem using a song. Write down the url link to the video that you have found. Write two paragraphs as an evaluation of this video in comparison to The Best Pythagorean Theorem Rap Ever. Ideas of elements to consider: What does it do well? Why? Does it reinforce key points? How? How could the video be improved? Literacy including spelling and grammar and cohesion Evaluation of at least two elements of the song that make it successful (or not) in its aim of teaching Pythagoras Theorem Unique idea to improve the song Page Assignment 1 Year 8 Mathematics
13 Technology We will use Sway for the tasks in this section. 1. Log into Student portal 2. Open Microsoft Office 365 (under the Learning section) 3. Open Sway. 4. Click Create New 5. Add a title, Special Quadrilaterals. When you have completed your chosen tasks: 1. Click on Share 2. Make sure the switch is on the share side. 3. Copy the url and include it in your assignment submission. 31) List Special Quadrilaterals Add a text card to your Sway and list the six special quadrilaterals. Accurate list of six special quadrilaterals 32) Find Parallelograms Add an image card to your Sway and search for and paste an image of a building that is shaped like a parallelogram. Correct image of a building 33) Cargo Boxes Play the game Cargo Boxes ( until you complete level 4. Take screenshots of your bridge designs for each completed level and add them to your Sway. Evidence of level 1 & 2 complete Evidence of level 3 & 4 complete 34) Good Bridge Design Search the internet for bridge designs and add 3 different bridge styles to your Sway. Add a text card and answer, What shape is repeated in all the designs that you have discovered? 3 unique bridge designs Correct description of repeated shape Page Assignment 1 Year 8 Mathematics
14 35) Bad Bridge Design Use the game Cargo Boxes ( to test bridges made in the shape of parallelogram. Add a screenshot to your Sway of your design. Write two paragraphs explaining why a parallelogram shape does or does not work. Accurate images of parallelogram bridges Literacy including spelling and grammar Correct explanation outlining more than 1 factor 36) Cargo Boxes Use your answer to activity 32 for this task. Add a text card to your Sway with the answer to these questions: Which part of the building is under the most stress from weight? How has the architect reinforced this part of the building? Identify weak point of a building Literacy including spelling and grammar Accurate description of strengthening (or assumed strengthening if not visible) Overall marking comments Result /30 Page Assignment 1 Year 8 Mathematics
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